There is an article by G. W. Montgomery, written in 1996, about mapping of the horn (HO) locus in sheep. Horn development can range from fully developed large curly horns, firmly attached to the frontal bone, to polled or hornless animals with no horn development, and concave depressions in the skull. Many intermediate types are possible that may or may not be attached to the frontal bone.

The presence of horns is controlled by a single autosomal locus (HO) with three alleles:

Another autosomal locus with alleles that interact with the HO locus, resulting in the growth of scurs or aberrant horns in rams.

It's interesting to note that in cold climates, heat loss through the horn surface may be substantial. The internal core of the horn contains many blood vessels, while the outer keratin sheath presumably offers little in the way of insulation. Because horns are living tissue, the bony core and surround vascular tissue cannot be allowed to freeze because of its proximity to the brain. Considerable amounts of heat can be lost through the horn surface, particularly in large horned species. Horns are thought to play a thermoregulator role as heat dissipation structures and benefit the animal in hot weather, but this heat loss may be detrimental in winter. The largest surface area that the animal can afford to sustain through the winter may limit horn size. The length of the vascular bony horn core relative to overall horn length may be smaller for species found in cold climates than for species inhabiting warm climates.

If the bodies of the horns spiral in opposite directions, they're "conjugate", one being the mirror image of the other, and they should be balanced or symmetrical. Each horn normally has three borders and three surfaces (back, front, and side). These divisions are more difficult to see in a round horn versus the angular type. During growth, many primary or subannual horn rings are formed which resemble wrinkles, ripples, or slight ridges; these are separated by a complementary series of shallow primary or subannual horn grooves. There are deeper secondary or annual horn grooves that occur at approximately yearly intervals due to cessation of growth in winter, periods of drought, or mating activity. Hand-fed rams, removed from their natural environment, and raised under artificial conditions, lack these secondary grooves.